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<div class="title">PolynomialUtils.h</div>  </div>
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<div class="contents">
<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="comment">// This file is part of Eigen, a lightweight C++ template library</span></div>
<div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;<span class="comment">// for linear algebra.</span></div>
<div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;<span class="comment">// Copyright (C) 2010 Manuel Yguel &lt;manuel.yguel@gmail.com&gt;</span></div>
<div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;<span class="comment">// This Source Code Form is subject to the terms of the Mozilla</span></div>
<div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;<span class="comment">// Public License v. 2.0. If a copy of the MPL was not distributed</span></div>
<div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160;<span class="comment">// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.</span></div>
<div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160; </div>
<div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160;<span class="preprocessor">#ifndef EIGEN_POLYNOMIAL_UTILS_H</span></div>
<div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160;<span class="preprocessor">#define EIGEN_POLYNOMIAL_UTILS_H</span></div>
<div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160; </div>
<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160;<span class="preprocessor">#include &quot;./InternalHeaderCheck.h&quot;</span></div>
<div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160; </div>
<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;<span class="keyword">namespace </span><a class="code" href="namespaceEigen.html">Eigen</a> { </div>
<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160; </div>
<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> Polynomials, <span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;<span class="keyword">inline</span></div>
<div class="line"><a name="l00030"></a><span class="lineno"><a class="line" href="group__Polynomials__Module.html#gaadbf059bc28ce1cf94c57c1454633d40">   30</a></span>&#160;T <a class="code" href="group__Polynomials__Module.html#gaadbf059bc28ce1cf94c57c1454633d40">poly_eval_horner</a>( <span class="keyword">const</span> Polynomials&amp; poly, <span class="keyword">const</span> T&amp; x )</div>
<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;{</div>
<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;  T val=poly[poly.size()-1];</div>
<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;  <span class="keywordflow">for</span>(DenseIndex i=poly.size()-2; i&gt;=0; --i ){</div>
<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;    val = val*x + poly[i]; }</div>
<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;  <span class="keywordflow">return</span> val;</div>
<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;}</div>
<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160; </div>
<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> Polynomials, <span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;<span class="keyword">inline</span></div>
<div class="line"><a name="l00048"></a><span class="lineno"><a class="line" href="group__Polynomials__Module.html#gadb64ffddaa9e83634e3ab0e3fd3664f5">   48</a></span>&#160;T <a class="code" href="group__Polynomials__Module.html#gadb64ffddaa9e83634e3ab0e3fd3664f5">poly_eval</a>( <span class="keyword">const</span> Polynomials&amp; poly, <span class="keyword">const</span> T&amp; x )</div>
<div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;{</div>
<div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="codeRef" href="../structEigen_1_1NumTraits.html">NumTraits&lt;T&gt;::Real</a> Real;</div>
<div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160; </div>
<div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;  <span class="keywordflow">if</span>( numext::abs2( x ) &lt;= Real(1) ){</div>
<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;    <span class="keywordflow">return</span> <a class="code" href="group__Polynomials__Module.html#gaadbf059bc28ce1cf94c57c1454633d40">poly_eval_horner</a>( poly, x ); }</div>
<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;  {</div>
<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;    T val=poly[0];</div>
<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;    T inv_x = T(1)/x;</div>
<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;    <span class="keywordflow">for</span>( DenseIndex i=1; i&lt;poly.size(); ++i ){</div>
<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;      val = val*inv_x + poly[i]; }</div>
<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160; </div>
<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;    <span class="keywordflow">return</span> numext::pow(x,(T)(poly.size()-1)) * val;</div>
<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;  }</div>
<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;}</div>
<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160; </div>
<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> Polynomial&gt;</div>
<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;<span class="keyword">inline</span></div>
<div class="line"><a name="l00077"></a><span class="lineno"><a class="line" href="group__Polynomials__Module.html#ga375e3ea1f370fb76dfe0f43a89b95926">   77</a></span>&#160;<span class="keyword">typename</span> <a class="codeRef" href="../structEigen_1_1NumTraits.html">NumTraits&lt;typename Polynomial::Scalar&gt;::Real</a> <a class="code" href="group__Polynomials__Module.html#ga375e3ea1f370fb76dfe0f43a89b95926">cauchy_max_bound</a>( <span class="keyword">const</span> Polynomial&amp; poly )</div>
<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;{</div>
<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;  <span class="keyword">using</span> std::abs;</div>
<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> Polynomial::Scalar Scalar;</div>
<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="codeRef" href="../structEigen_1_1NumTraits.html">NumTraits&lt;Scalar&gt;::Real</a> Real;</div>
<div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160; </div>
<div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;  eigen_assert( Scalar(0) != poly[poly.size()-1] );</div>
<div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;  <span class="keyword">const</span> Scalar inv_leading_coeff = Scalar(1)/poly[poly.size()-1];</div>
<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;  Real cb(0);</div>
<div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160; </div>
<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;  <span class="keywordflow">for</span>( DenseIndex i=0; i&lt;poly.size()-1; ++i ){</div>
<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;    cb += <a class="codeRef" href="../namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(poly[i]*inv_leading_coeff); }</div>
<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;  <span class="keywordflow">return</span> cb + Real(1);</div>
<div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;}</div>
<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160; </div>
<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> Polynomial&gt;</div>
<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;<span class="keyword">inline</span></div>
<div class="line"><a name="l00100"></a><span class="lineno"><a class="line" href="group__Polynomials__Module.html#gab076afbdba0e9298a541cc4e8cc7506b">  100</a></span>&#160;<span class="keyword">typename</span> <a class="codeRef" href="../structEigen_1_1NumTraits.html">NumTraits&lt;typename Polynomial::Scalar&gt;::Real</a> <a class="code" href="group__Polynomials__Module.html#gab076afbdba0e9298a541cc4e8cc7506b">cauchy_min_bound</a>( <span class="keyword">const</span> Polynomial&amp; poly )</div>
<div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;{</div>
<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160;  <span class="keyword">using</span> std::abs;</div>
<div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> Polynomial::Scalar Scalar;</div>
<div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="codeRef" href="../structEigen_1_1NumTraits.html">NumTraits&lt;Scalar&gt;::Real</a> Real;</div>
<div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160; </div>
<div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160;  DenseIndex i=0;</div>
<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;  <span class="keywordflow">while</span>( i&lt;poly.size()-1 &amp;&amp; Scalar(0) == poly(i) ){ ++i; }</div>
<div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;  <span class="keywordflow">if</span>( poly.size()-1 == i ){</div>
<div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;    <span class="keywordflow">return</span> Real(1); }</div>
<div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160; </div>
<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;  <span class="keyword">const</span> Scalar inv_min_coeff = Scalar(1)/poly[i];</div>
<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;  Real cb(1);</div>
<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;  <span class="keywordflow">for</span>( DenseIndex j=i+1; j&lt;poly.size(); ++j ){</div>
<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160;    cb += <a class="codeRef" href="../namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(poly[j]*inv_min_coeff); }</div>
<div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;  <span class="keywordflow">return</span> Real(1)/cb;</div>
<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;}</div>
<div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160; </div>
<div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> RootVector, <span class="keyword">typename</span> Polynomial&gt;</div>
<div class="line"><a name="l00129"></a><span class="lineno"><a class="line" href="group__Polynomials__Module.html#gafbc3648f7ef67db3d5d04454fc1257fd">  129</a></span>&#160;<span class="keywordtype">void</span> <a class="code" href="group__Polynomials__Module.html#gafbc3648f7ef67db3d5d04454fc1257fd">roots_to_monicPolynomial</a>( <span class="keyword">const</span> RootVector&amp; rv, Polynomial&amp; poly )</div>
<div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;{</div>
<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160; </div>
<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> Polynomial::Scalar Scalar;</div>
<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160; </div>
<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;  poly.setZero( rv.size()+1 );</div>
<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;  poly[0] = -rv[0]; poly[1] = Scalar(1);</div>
<div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;  <span class="keywordflow">for</span>( DenseIndex i=1; i&lt; rv.size(); ++i )</div>
<div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160;  {</div>
<div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160;    <span class="keywordflow">for</span>( DenseIndex j=i+1; j&gt;0; --j ){ poly[j] = poly[j-1] - rv[i]*poly[j]; }</div>
<div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160;    poly[0] = -rv[i]*poly[0];</div>
<div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160;  }</div>
<div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160;}</div>
<div class="line"><a name="l00142"></a><span class="lineno">  142</span>&#160; </div>
<div class="line"><a name="l00143"></a><span class="lineno">  143</span>&#160;} <span class="comment">// end namespace Eigen</span></div>
<div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160; </div>
<div class="line"><a name="l00145"></a><span class="lineno">  145</span>&#160;<span class="preprocessor">#endif </span><span class="comment">// EIGEN_POLYNOMIAL_UTILS_H</span></div>
<div class="ttc" id="agroup__Polynomials__Module_html_ga375e3ea1f370fb76dfe0f43a89b95926"><div class="ttname"><a href="group__Polynomials__Module.html#ga375e3ea1f370fb76dfe0f43a89b95926">Eigen::cauchy_max_bound</a></div><div class="ttdeci">NumTraits&lt; typename Polynomial::Scalar &gt;::Real cauchy_max_bound(const Polynomial &amp;poly)</div><div class="ttdef"><b>Definition:</b> PolynomialUtils.h:77</div></div>
<div class="ttc" id="agroup__Polynomials__Module_html_gaadbf059bc28ce1cf94c57c1454633d40"><div class="ttname"><a href="group__Polynomials__Module.html#gaadbf059bc28ce1cf94c57c1454633d40">Eigen::poly_eval_horner</a></div><div class="ttdeci">T poly_eval_horner(const Polynomials &amp;poly, const T &amp;x)</div><div class="ttdef"><b>Definition:</b> PolynomialUtils.h:30</div></div>
<div class="ttc" id="agroup__Polynomials__Module_html_gab076afbdba0e9298a541cc4e8cc7506b"><div class="ttname"><a href="group__Polynomials__Module.html#gab076afbdba0e9298a541cc4e8cc7506b">Eigen::cauchy_min_bound</a></div><div class="ttdeci">NumTraits&lt; typename Polynomial::Scalar &gt;::Real cauchy_min_bound(const Polynomial &amp;poly)</div><div class="ttdef"><b>Definition:</b> PolynomialUtils.h:100</div></div>
<div class="ttc" id="agroup__Polynomials__Module_html_gadb64ffddaa9e83634e3ab0e3fd3664f5"><div class="ttname"><a href="group__Polynomials__Module.html#gadb64ffddaa9e83634e3ab0e3fd3664f5">Eigen::poly_eval</a></div><div class="ttdeci">T poly_eval(const Polynomials &amp;poly, const T &amp;x)</div><div class="ttdef"><b>Definition:</b> PolynomialUtils.h:48</div></div>
<div class="ttc" id="agroup__Polynomials__Module_html_gafbc3648f7ef67db3d5d04454fc1257fd"><div class="ttname"><a href="group__Polynomials__Module.html#gafbc3648f7ef67db3d5d04454fc1257fd">Eigen::roots_to_monicPolynomial</a></div><div class="ttdeci">void roots_to_monicPolynomial(const RootVector &amp;rv, Polynomial &amp;poly)</div><div class="ttdef"><b>Definition:</b> PolynomialUtils.h:129</div></div>
<div class="ttc" id="anamespaceEigen_html"><div class="ttname"><a href="namespaceEigen.html">Eigen</a></div><div class="ttdoc">Namespace containing all symbols from the Eigen library.</div></div>
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